Question

A more realistic way than sampling continuous signals x(t) with
a train of δ-impulses is via the
use of a train of rectangular pulses p(t). The system that performs
this sampling is called S/H
(Sample and Hold) system and produces the signal x0(t)
from x(t) like in Figure 7.5.

Figure
7.5

a) Sketch the impulse response h(t) of the S/H system (Figure
7.6(a))

Figure 7.6
(a)

b) Show that the FT of the S/H system is given by Eq. 7.7

Eqn
7.7

c) Show that if we want to get the continuous signal x(t) back
from the sampled signal x0(t)
we have to use a filter (system) with frequency response Hr(jω)
given by Eq. 7.8 (this
whole process is depicted in Fig. 7.7 – the Hr(jω) is plotted in
Fig. 7.8).